On some correspondences between relational structures and algebras
On some properties a projective model class passes on to the generated axiomatic class.
On some ternary operations in knot theory
We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, we obtain the relations from the knot group, and from the core group. Using the ternary operator approach, we generalize the Dehn presentation of the knot group to extra loops, and a similar presentation for the core group to the variety of Moufang loops.
On synchronized relatively full embeddings and -universality
On the characterisation of Mal'tsev and Jónsson-Tarski algebras
There are very strong parallels between the properties of Mal'tsev and Jónsson-Tarski algebras, for example in the good behaviour of centrality and in the factorization of direct products. Moreover, the two classes between them include the majority of algebras that actually arise 'in nature'. As a contribution to the research programme building a unified theory capable of covering the two classes, along with other instances of good centrality and factorization, the paper presents a common framework...
On the characterization of Jonsson-Tarski and of subtractive varieties
On the congruence lattice of stable algebras with definability of compact congruences
On the failure of Birkhoff's theorem for locally small based equational categories of algebras
On the lattices of quasivarieties of differential groupoids
The main result of Romanowska A., Roszkowska B., On some groupoid modes, Demonstratio Math. 20 (1987), no. 1–2, 277–290, provides us with an explicit description of the lattice of varieties of differential groupoids. In the present article, we show that this variety is -universal, which means that there is no convenient explicit description for the lattice of quasivarieties of differential groupoids. We also find an example of a subvariety of differential groupoids with a finite number of subquasivarieties....
On the membership problem for pseudo-varieties of commutative semigroups.
On the power semigroup of a finite semigroup
On the quasivarieties generated by finite semigroups.
On the semidirect product of the pseudovariety of semilattices by a locally finite pseudovariety of groups
On the structure of equationally complete varieties. I
On the structure of semilattice sums
On universality of semigroup varieties
A category is called -determined if every set of non-isomorphic -objects such that their endomorphism monoids are isomorphic has a cardinality less than . A quasivariety is called -universal if the lattice of all subquasivarieties of any quasivariety of finite type is a homomorphic image of a sublattice of the lattice of all subquasivarieties of . We say that a variety is var-relatively alg-universal if there exists a proper subvariety of such that homomorphisms of whose image does...
Operads and algebraic geometry.
Optimal natural dualities for some quasivarities of distributive double -algebras.
Orthomodular lattices with fully nontrivial commutators
An orthomodular lattice is said to have fully nontrivial commutator if the commutator of any pair is different from zero. In this note we consider the class of all orthomodular lattices with fully nontrivial commutators. We show that this class forms a quasivariety, we describe it in terms of quasiidentities and situate important types of orthomodular lattices (free lattices, Hilbertian lattices, etc.) within this class. We also show that the quasivariety in question is not a variety answering...
Orthomodular lattices with state-separated noncompatible pairs
In the logico-algebraic foundation of quantum mechanics one often deals with the orthomodular lattices (OML) which enjoy state-separating properties of noncompatible pairs (see e.g. , and ). These properties usually guarantee reasonable “richness” of the state space—an assumption needed in developing the theory of quantum logics. In this note we consider these classes of OMLs from the universal algebra standpoint, showing, as the main result, that these classes form quasivarieties. We also illustrate...